cp's OEIS Frontend

A102815 "False so far" sequence.

%I A102815 #13 Dec 19 2022 16:54:08
%S A102815 11,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,
%T A102815 42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,
%U A102815 65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,101
%N A102815 "False so far" sequence.
%C A102815 The last digit of a(n) is regarded as a glyph and the preceding digits as a number. So "11" reads [one "1"] and "20" [two "0"] - which are both false statements here: there is not one "1" glyph so far in the sequence when [11] is read, but two; and there are not two "0" glyph when [20] is read, but only one. The sequence is built with [a(n+1)-a(n)] minimal and a(n+1) always "false so far". This explains why the sequence doesn't begin with [10]: its statement would be true.
%C A102815 After integer [20] the sequence matches A000027 without [100] -- because [100] would be "true so far".
%C A102815 [This seems to imply that the sequence contains all numbers >= 20 except 100. - _N. J. A. Sloane_, Aug 22 2011]
%C A102815 The above is correct, and a(n) = n + 19 for n > 81. Proof: It is enough to show that all terms 101 to N are in the sequence, that N >= 101 + 100, and that the count of digits through N is at least floor(N/10) + 11 for each decimal digit. Note that, from the last two digits, the count of each digit increases by at least 20 every 100 numbers, but the required number increases by only 10. Then by a count of the digits, N = 210 suffices. It is easy to check that the remaining conditions are satisfied. - _Charles R Greathouse IV_, Dec 19 2022
%H A102815 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A102815 a(n) = n + 19 for n > 81, see comments. - _Charles R Greathouse IV_, Dec 19 2022
%o A102815 (PARI) a(n)=n+if(n>81,19,n>1,18,10) \\ _Charles R Greathouse IV_, Dec 19 2022
%Y A102815 Cf. A102357.
%K A102815 base,easy,nonn
%O A102815 1,1
%A A102815 _Eric Angelini_, Feb 26 2005